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Necessary Adjustments

Deviations for biased cash flows

Cash flows vary, and traditional approaches need to take into consideration the downside or cessation probability; otherwise, the value of the entity is overstated. Setting the probabilities of “downside” and “cessation” risk drives the appraiser’s efforts in adjusting for biased cash flows. This article presents an approach that can be used to adjust the cash flow.


Deviations from the Expected

In valuation, biased estimates of cash flows are commonly submitted to the appraiser by management, counsel, or others as the best estimates of the future. “Biased cash flows” are those that are not genuinely expected. An expected cash flow is one which has been adjusted for downside potential via some type of probability-weighting exercise. However, management’s view is generally—and naturally—skewed toward the positive and rarely tempered by downside outcomes.

Perhaps the most common method for creating expected cash flows is to create multiple scenarios which represent the full range of potential outcomes, then weight each scenario with a probability. In many cases, though, appraisers are not presented with the probability-weighted estimates of the future. In situations where one single estimate of the future is provided, the appraiser can return the cash flow estimates to management and request that they please “try again” or the appraiser can undertake a number of tasks such as:

  1. Adjust the cash flows by “watering-down” management’s estimates
  2. Adjust “for” bias in the existing cash flows

Employ a number of enhanced analytical tools. In situations where management input is not available to the appraiser (litigation support settings, appraisal review, retrospective appraisals, etc.), the latter options are often the best and only choices available

The Natural Optimism of Management

Managerial optimism is a necessary component when projecting the future for a project or an enterprise, but in situations where idiosyncratic risk of cash flows is prevalent, a valuation analysis might underestimate the discount rate or overstate the net present value. [See Saha, Valuation of Cash Flows with Time-Varying Cessation Risk]. Idiosyncratic risk –often referred to either as unsystematic, residual risk, or diversifiable risk, because these risks can, theoretically, be eliminated through diversification– is risk that is specific to an asset or a small group of assets. In fact, it has been suggested that equity-based compensation arrangements expose managers to idiosyncratic risk that “distorts the manager’s discount rate and, in turn, investment and financing decisions.” [See Glover, Levine, Idiosyncratic Risk and the Manager]. Even in situations where management has taken care to create multiple probability-weighted cash flow estimates, (traditional base, best-, and worst-case, scenarios), “it is not unusual for the forecast to be aspirational, rather than expectational.” [See Grabowski, Harrington, Nunes, 2014 Valuation Handbook, Guide to Cost of Capital, Duff & Phelps, p. 6-6].

Downside Realities

“Based on mortality research of start-up firms (VC or PE-backed) across various industries, Saha (2014) reports that cessation risk is not fixed, but that it varies and declines with time. Cessation risk for many enterprises is material, and with empirical evidence as support, should be modeled.”

There are clear examples where even management’s most pessimistic scenarios tend to have an upward bias— because these pessimistic scenarios are sometimes premised on successful (or less dire) outcomes. These firms, like all enterprises, operate with some probability of “downside” outcomes, but even pessimistic, worst-case scenarios can overestimate net present value (NPV) if the downside is not a drastic enough prognostication of failure. Venture capitalists know of failure scenarios and will often utilize very high discount rates (as high as 80 percent) in their Venture Capital (VC) Method estimates of residual values as one way of capturing failure risks. However, these upward discount rate adjustments are often referred to as “fudge-factors, which managers use because they fail to give bad outcomes their due weight in cash flow forecasts.” [See Ruback, Downsides and DCF: Valuing Biased Cash Flow Forecasts].

The start-up and early-stage venture-backed firm wrestles with a special case of the downside scenario: the risk of “cessation.” Cessation risk is especially likely in the first years of an enterprise. Knaup (2005) analyzed business survival statistics from 1998 to 2002, reporting that 80 percent of small businesses survive their first year, 65 percent survive their second year, and only 55 percent survive their third year. A study of technology and biotechnology venture-backed firms by Hall and Woodward (2010) shows that 65 percent of the venture-backed companies studied failed to achieve an initial public offering (IPO), an acquisition, or other successful exit. Based on mortality research of start-up firms (VC- or private equity (PE)-backed) across various industries, Saha (2014) reports that cessation risk is not fixed, but that it varies and declines with time. Cessation risk for many enterprises is material, and with empirical evidence as support, should be modeled.

Adjustments to Biased-Cash Flows

Step One: Qualitative Risk-Assessment (Downside & Cessation)

Appraisers are curious about risk and reward. One of the two key elements to an Income Approach is our estimation of a risk-adjusted discount rate (the other being the cash flow estimates themselves). In the case of an early-stage, VC-backed company (suppose a firm that has recently raised $15 million in an initial A-round investment), the downside projection exercise is comparatively straightforward. The probability of complete cessation for such a firm is high, and many appraisers are able to point to empirical evidence of survival rates for VC-backed firms in estimating such.

The real work begins in creating downside scenarios for the going-concern enterprise; and despite management’s insistence that downside or cessation is very unlikely, recent history suggests that, to yield credible appraisal analyses, aspirational views must be tempered by downside outcomes and cessation considerations.

Firstly, the appraiser can identify all risks faced by the enterprise: industry, company, economy, technological, and so on. Then, the appraiser considers which of the identified risk factors in each category is idiosyncratic (also referred to as unsystematic, diversifiable, or firm-specific) for the enterprise. Some caution may be required to be certain that the identified downside/cessation risks conceptually fit within the appraiser’s estimates for cost-of-capital, i.e., do not confuse systematic with unsystematic and present a risk double-counting situation. Firm-specific risk is considered unsystematic and is risk to which only specific agents or industries are vulnerable (and is uncorrelated with broad market returns). Systematic risk is vulnerability to events which affect aggregate outcomes such as broad market returns. Appraisers often utilize the Capital Asset Pricing Model (CAPM) to estimate a cost of capital for the enterprise or asset. CAPM includes the appraisers’ estimates for beta, which represents an asset’s exposure to systematic risk.

The appraiser can interview management to determine if these firm-specific risks have been included in their projected cash flows. In the experience of many, unless the firm is distressed, management does not spend much mental energy in thinking of drastic downside scenarios for their enterprise, division, or asset portfolio. Managers and business owners are natural optimists, even when faced with a dire situation.

Step Two: Adjustments to Biased Cash Flows

Setting the probabilities of downside and cessation risk drives the appraiser’s efforts in adjusting for biased cash flows. Ruback1 provides a framework where the biased forecast is adjusted by a downside adjustment that can be temporary, permanent, or attenuated. An example of a temporary downside would be represented by an agricultural drought year, while a permanent downside could exist if a technology failure or obsolescence affects current and future period cash flows so drastically that it leaves the firm without alternative product/service offerings. It is possible that BlackBerry has operated in a permanent downside scenario for the past several years due to its failure to create compelling wireless telephony products in a highly competitive market.

Adjusting for Bias via Ruback’s Downside Adjustments2

Ruback’s Temporary-Downside: The expected cash flow in each period t, E(X ) is: E(X )t = (1-λ )X = E(X ), where there is a (1-λ) probability of a cash flow of X and a λ probability of a cash flow of zero in period t. The Adjusted Cash Flow = X(1-λ)/k. The adjusted cash flow formula, where the downside has non-zero values, is also available to the analyst. Ruback’s temporary downside assumes that future cash flows are not affected by the down period. The author suggests that a temporary downside adjustment should be reflected by changing the cash flow while keeping the discount rate unchanged. On examination, what Ruback is expressing is the common probability-adjustment process that is expressed mathematically.

Ruback’s Permanent-Downside: In the permanent scenario, all following periods experience a downside, expressed as: Et(X) = (1−λ)^t * X. In contrast to the temporary downside, when the downside is assumed to be permanent, the probability that the downside will occur is added to the cost of capital. The Adjusted Cash Flow = X(1-λ)/(k+λ). Note that for lower discount rates, k, the larger is the value consequence of assuming a permanent omitted downside. A permanent downside scenario may not be entirely realistic, or empirically supported, as illustrated by Saha’s declining cessation risk findings, noted above.

Ruback’s Hybrid-Downside: Scenarios where a once dominant market leader loses position (and, once lost, will generate lower expected cash flows into the future) can be captured with a hybrid approach. The probability of a downside occurring is λ and remains λ until the downside occurs. Once the downside occurs, there can be a permanent shift downward in the probability of a subsequent downside, γ. The probability of achieving this subsequent cash flow is (1-γ). The expected cash flow would be: E(Xt) = (1-λ)^t*X + (1-γ)*X*(1-(1-λ)^(t-1)).

Ruback’s Attenuation-Downside: In cases where the probability of a downside declines over the life of the project, asset, or enterprise, Ruback suggests “attenuating” the downside λ by a factor that he defines as (1 – δ) where δ < 1. The impact of this attenuation—and also of the permanent downside—are more significant in the early periods of the life of the annuity or an asset. (See Ruback’s article for graphical illustrations).

Step Three: Enhanced Methods

The process of estimating probability-weighted cash flows represents a scenario analysis, which allows the appraiser to better sense the effect of risk on value. While these scenarios provide the appraiser with risk-reward insights, they are not always the most informative because they provide a snapshot of the riskiness of the asset only if the scenarios cover the spectrum of possibilities. When outcomes can take on any of a very large number of potential values or the risk is continuous (rather than discrete as is the case with scenario analysis), these scenario analyses become much more difficult to construct.

Probability-Tree and Decision-Tree Analyses

When true “expected” cash flow estimates are not available, then an appraiser’s downward adjustments to biased cash flow estimates can produce credible estimates. However, additional analytical methods are available to the appraiser.

One option available to the appraiser is to create a probability-tree for use in a Probability-Weighted-Expected-Return-Method (PWERM). Probability trees can be used for modeling independent events or conditional probabilities. PWERM is a valuation method based upon an analysis of various future outcomes, such as an IPO, merger or sale, dissolution, or continued operation as a private enterprise until a later exit date. The future allocated value is based upon the probability-weighted present values of expected future investment returns, considering each of the possible outcomes available to the enterprise, as well as the rights of each security class. Inherent in the PWERM are probability estimates for various outcomes.

The PWERM concept can be applied to Income Approach scenarios as well and is especially useful in the valuation of choices, where management has several monetizing options available for an asset or enterprise. Each monetizing scenario can include expected cash flow estimates (base, best- and worst-case) or the present value of several different monetizing scenarios, each weighted by probability estimates. Care is needed in the selection of discount rates used in the PWERM Approach. Many appraisers use a risk-free rate (Rf) to derive the present value of future expected values, under the assumption that the probability weightings have already accounted for projection risk.

In some projects or enterprises, risk is not only discrete, but sequential. For an asset or project to have value, it has to pass through a series of steps, or tests, with failure at each step potentially reducing the value of the asset to zero, e.g., a pharmaceutical drug trial. Decision Trees Analysis (DTA) allows the appraiser to consider the risks at each step and model the likely management response to outcomes at each step. DTA provides a highly effective structure within which the appraiser can lay out options and investigate the possible outcomes and the probabilities of achieving them. DTA also helps to form a balanced picture of the risks and rewards associated with each possible course of action. Decision trees are best suited to situations where risk is sequential because they look at risk as discrete outcomes: success or failure. In situations where risk is continuous, a simulation can provide a fuller picture of the risk in an asset or enterprise.


Most risks to an enterprise can generate hundreds of possible outcomes, and simulations allow the appraiser more flexibility in dealing with inherent uncertainty. In a simulation, the appraiser estimates distributions of values for several parameters, or variables, in the analysis (growth, market-share, operating margin, etc.). Once the key, value-driving variables are selected, a probability distribution is chosen for each by referencing historical, cross-section, or statistical data. A simulation then calculates results over and over, each time using a different set of random values from the probability functions.

A very common simulation used by business appraisers is the Monte Carlo Method, which comprises a broad class of computation algorithms that rely on repeated random sampling to obtain numerical results and allow users to account for risk in quantitative analysis and decision making. For the appraiser, the output provides insights into the range—or distribution—of results. A powerful Monte Carlo simulator illustrates input sensitivities: how sensitive is value to changes in revenue growth, operating margin, or some other parameter.

Simulations yield great looking output, even if the inputs are entirely random. For simulations to have value, however, the distributions chosen for the inputs should be based on analysis and empirical data, not guesswork.






Mark Krickovich is the owner/founder of MK Appraisal Group, a boutique business valuation and consulting firm located in Portland, OR, with a virtual office in Sacramento, CA. He can be reached via e-mail at and at (503)319-4191.

1*Richard Ruback, “Downside and DCF: Valuing Biased Cash Flow Forecasts,” Journal of Applied Corporate Finance 23(2) (Spring 2011): 8-17. Copyright © 2011 Morgan Stanley. Used with permission via license agreement between MK Appraisal Group and John Wiley and Sons.


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